We analyze the time- and frequency-domain response of directional-coupler traveling-wave optical modulators (DCTWOM) in which the optical and electrical velocities are not matched. We demonstrate for traveling-wave modulators that a directional-coupler device is intrinsically faster, by nearly a factor of for the same drive, than an interferometric device of the same length. We also show, that because of nonlinearities in the directional-coupler response, the switching speed inferred through a numerical analysis in the frequency domain underestimates the impulse response derived directly in the time domain. For a directional-coupler traveling-wave modulator based in LiNbO3, the Fourier transformation of the impulse response (33 ps/cm FWHM) indicates a characteristic length-bandwidth product of 15 GHz. cm when microwave loss is neglected. When realistic frequency-dependent losses are included in the frequency-domain calculations, we conclude that a 1-cm-long directional coupler in LiNbO3has a large signal 3-dB bandwidth in excess of 10 GHz. We determine the optical response to closely spaced electrical pulses, in order to evaluate the signal encoding bit rate capabilities of the device and its relation to the frequency bandwidth.